The government is paying back $721 million to 373,000 people chased for debts through the unlawful program.

"The government has great regrets about any pain or injury that has been caused here, but those are issues we are still working through and we're making it right," Mr Morrison told reporters in Sydney on Monday.

The scrapped scheme matched Australian Taxation Office and Centrelink data to claw back overpaid welfare payments.

Mr Morrison said Labor and coalition governments had both used income averaging.

He said the government needed to be diligent about chasing down taxpayers' money if there were welfare overpayments.

"But you've got to do it in the lawful way and we will ensure to continue to do that with our projects going forward," the prime minister said.

About 470,000 debts were raised through the defunct welfare scheme, which is now the subject of a class action challenge.

The controversial system was ruled unlawful last year, with the Federal Court saying Centrelink could not have been satisfied the debt was correct.

Labor frontbencher Bill Shorten is demanding an apology from the coalition.

"This is pretty, pretty bloody outrageous what the government's done," he told Sky News.

"This is not another day at the office and it's caused a lot of hardship to ordinary people who are vulnerable."

Australian Associated Press